Question

If a2+1=4a,what is the value of a4+1/a4

Answer 1

$\large{ \text{ \underline{Given}}}$

$\sf{ {a}^{2} + 1 = 4a}$

$\sf{ = > a + \frac{1}{a} = 4 } \: \: \mathcal{ \blue{(Dividing \: "a"\: in \: both \: sides)}}$

$\large{ \underbrace{ \red{ \text{✿Solution}}}}$

${a}^{4} + \frac{1}{ {a}^{4} }$

$= ( {a}^{2} ) {}^{2} + (\frac{1}{ {a}^{2} } ) {}^{2}$

$= ( {a}^{2} + \frac{1}{ {a}^{2} } ) {}^{2} - 2 \times {a}^{2} \times \frac{1}{ {a}^{2} }$

$= ((a) {}^{2} + (\frac{1}{a} ) {}^{2} ) {}^{2} - 2$

$= ( (a + \frac{1}{a} ) {}^{2} - 2 \times a \times \frac{1}{a} ) {}^{2} - 2$

$= ( 4 {}^{2} - 2) {}^{2} - 2$

$= (16 - 2) {}^{2} - 2$

$= 196 - 2$

$\sf{ \orange{ \boxed{ = 194}}}$

Hope this helps!

Answer 2

Answer:

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